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    //! **Ignore me!** This module is for things that are conceptually private but that must
    //! be made public for typenum to work correctly.
    //!
    //! Unless you are working on typenum itself, **there is no need to view anything here**.
    //!
    //! Certainly don't implement any of the traits here for anything.
    //!
    //!
    //! Just look away.
    //!
    //!
    //! Loooooooooooooooooooooooooooooooooook awaaaaaaaaaaaayyyyyyyyyyyyyyyyyyyyyyyyyyyyy...
    //!
    //!
    //! If you do manage to find something of use in here, please let me know. If you can make a
    //! compelling case, it may be moved out of __private.
    //!
    //! Note: Aliases for private type operators will all be named simply that operator followed
    //! by an abbreviated name of its associated type.
    //!

    #![doc(hidden)]

    // use ::{Sub};
    use bit::{B0, B1, Bit};
    use uint::{UInt, UTerm, Unsigned};

    /// Convenience trait. Calls `Invert` -> `TrimTrailingZeros` -> `Invert`
    pub trait Trim {
        type Output;
    }
    pub type TrimOut<A> = <A as Trim>::Output;

    /// Gets rid of all zeros until it hits a one.

    // ONLY IMPLEMENT FOR INVERTED NUMBERS!
    pub trait TrimTrailingZeros {
        type Output;
    }
    pub type TrimTrailingZerosOut<A> = <A as TrimTrailingZeros>::Output;

    /// Converts between standard numbers and inverted ones that have the most significant
    /// digit on the outside.
    pub trait Invert {
        type Output;
    }
    pub type InvertOut<A> = <A as Invert>::Output;

    /// Doubly private! Called by invert to make the magic happen once its done the first step.
    /// The Rhs is what we've got so far.
    pub trait PrivateInvert<Rhs> {
        type Output;
    }
    pub type PrivateInvertOut<A, Rhs> = <A as PrivateInvert<Rhs>>::Output;

    /// Terminating character for `InvertedUInt`s
    pub enum InvertedUTerm {}

    /// Inverted `UInt` (has most significant digit on the outside)
    pub struct InvertedUInt<IU: InvertedUnsigned, B: Bit> {
        _marker: (IU, B),
    }

    /// Does the real anding for `UInt`s; `And` just calls this and then `Trim`.
    pub trait PrivateAnd<Rhs = Self> {
        type Output;
    }
    pub type PrivateAndOut<A, Rhs> = <A as PrivateAnd<Rhs>>::Output;

    /// Does the real xoring for `UInt`s; `Xor` just calls this and then `Trim`.
    pub trait PrivateXor<Rhs = Self> {
        type Output;
    }
    pub type PrivateXorOut<A, Rhs> = <A as PrivateXor<Rhs>>::Output;

    /// Does the real subtraction for `UInt`s; `Sub` just calls this and then `Trim`.
    pub trait PrivateSub<Rhs = Self> {
        type Output;
    }
    pub type PrivateSubOut<A, Rhs> = <A as PrivateSub<Rhs>>::Output;

    /// Used for addition of signed integers; `C = P.cmp(N)`
    /// Assumes `P = Self` is positive and `N` is negative
    /// where `P` and `N` are both passed as unsigned integers
    pub trait PrivateIntegerAdd<C, N> {
        type Output;
    }
    pub type PrivateIntegerAddOut<P, C, N> = <P as PrivateIntegerAdd<C, N>>::Output;

    pub trait PrivatePow<Y, N> {
        type Output;
    }
    pub type PrivatePowOut<A, Y, N> = <A as PrivatePow<Y, N>>::Output;

    /// Performs `Shl` on `Lhs` so that `SizeOf(Lhs) = SizeOf(Rhs)`
    /// Fails if `SizeOf(Lhs) > SizeOf(Rhs)`
    pub trait ShiftDiff<Rhs> {
        type Output;
    }
    pub type ShiftDiffOut<A, Rhs> = <A as ShiftDiff<Rhs>>::Output;

    /// Gives `SizeOf(Lhs) - SizeOf(Rhs)`
    pub trait BitDiff<Rhs> {
        type Output;
    }
    pub type BitDiffOut<A, Rhs> = <A as BitDiff<Rhs>>::Output;

    /// Inverted unsigned numbers
    pub trait InvertedUnsigned {
        fn to_u64() -> u64;
    }

    impl InvertedUnsigned for InvertedUTerm {
        fn to_u64() -> u64 {
            0
        }
    }

    impl<IU: InvertedUnsigned, B: Bit> InvertedUnsigned for InvertedUInt<IU, B> {
        fn to_u64() -> u64 {
            u64::from(B::to_u8()) | IU::to_u64() << 1
        }
    }

    impl Invert for UTerm {
        type Output = InvertedUTerm;
    }

    impl<U: Unsigned, B: Bit> Invert for UInt<U, B>
    where
        U: PrivateInvert<InvertedUInt<InvertedUTerm, B>>,
    {
        type Output = PrivateInvertOut<U, InvertedUInt<InvertedUTerm, B>>;
    }

    impl<IU: InvertedUnsigned> PrivateInvert<IU> for UTerm {
        type Output = IU;
    }

    impl<IU: InvertedUnsigned, U: Unsigned, B: Bit> PrivateInvert<IU> for UInt<U, B>
    where
        U: PrivateInvert<InvertedUInt<IU, B>>,
    {
        type Output = PrivateInvertOut<U, InvertedUInt<IU, B>>;
    }

    #[test]
    fn test_inversion() {
        type Test4 = <::consts::U4 as Invert>::Output;
        type Test5 = <::consts::U5 as Invert>::Output;
        type Test12 = <::consts::U12 as Invert>::Output;
        type Test16 = <::consts::U16 as Invert>::Output;

        assert_eq!(1, <Test4 as InvertedUnsigned>::to_u64());
        assert_eq!(5, <Test5 as InvertedUnsigned>::to_u64());
        assert_eq!(3, <Test12 as InvertedUnsigned>::to_u64());
        assert_eq!(1, <Test16 as InvertedUnsigned>::to_u64());
    }

    impl Invert for InvertedUTerm {
        type Output = UTerm;
    }

    impl<IU: InvertedUnsigned, B: Bit> Invert for InvertedUInt<IU, B>
    where
        IU: PrivateInvert<UInt<UTerm, B>>,
    {
        type Output = <IU as PrivateInvert<UInt<UTerm, B>>>::Output;
    }

    impl<U: Unsigned> PrivateInvert<U> for InvertedUTerm {
        type Output = U;
    }

    impl<U: Unsigned, IU: InvertedUnsigned, B: Bit> PrivateInvert<U> for InvertedUInt<IU, B>
    where
        IU: PrivateInvert<UInt<U, B>>,
    {
        type Output = <IU as PrivateInvert<UInt<U, B>>>::Output;
    }

    #[test]
    fn test_double_inversion() {
        type Test4 = <<::consts::U4 as Invert>::Output as Invert>::Output;
        type Test5 = <<::consts::U5 as Invert>::Output as Invert>::Output;
        type Test12 = <<::consts::U12 as Invert>::Output as Invert>::Output;
        type Test16 = <<::consts::U16 as Invert>::Output as Invert>::Output;

        assert_eq!(4, <Test4 as Unsigned>::to_u64());
        assert_eq!(5, <Test5 as Unsigned>::to_u64());
        assert_eq!(12, <Test12 as Unsigned>::to_u64());
        assert_eq!(16, <Test16 as Unsigned>::to_u64());
    }

    impl TrimTrailingZeros for InvertedUTerm {
        type Output = InvertedUTerm;
    }

    impl<IU: InvertedUnsigned> TrimTrailingZeros for InvertedUInt<IU, B1> {
        type Output = Self;
    }

    impl<IU: InvertedUnsigned> TrimTrailingZeros for InvertedUInt<IU, B0>
    where
        IU: TrimTrailingZeros,
    {
        type Output = <IU as TrimTrailingZeros>::Output;
    }

    impl<U: Unsigned> Trim for U
    where
        U: Invert,
        <U as Invert>::Output: TrimTrailingZeros,
        <<U as Invert>::Output as TrimTrailingZeros>::Output: Invert,
    {
        type Output = <<<U as Invert>::Output as TrimTrailingZeros>::Output as Invert>::Output;
    }

    // Note: Trimming is tested when we do subtraction.

    pub trait PrivateCmp<Rhs, SoFar> {
        type Output;
    }
    pub type PrivateCmpOut<A, Rhs, SoFar> = <A as PrivateCmp<Rhs, SoFar>>::Output;

    // Set Bit
    pub trait PrivateSetBit<I, B> {
        type Output;
    }
    pub type PrivateSetBitOut<N, I, B> = <N as PrivateSetBit<I, B>>::Output;

    // Div
    pub trait PrivateDiv<N, D, Q, R, I> {
        type Quotient;
        type Remainder;
    }

    pub type PrivateDivQuot<N, D, Q, R, I> = <() as PrivateDiv<N, D, Q, R, I>>::Quotient;
    pub type PrivateDivRem<N, D, Q, R, I> = <() as PrivateDiv<N, D, Q, R, I>>::Remainder;

    pub trait PrivateDivIf<N, D, Q, R, I, RcmpD> {
        type Quotient;
        type Remainder;
    }

    pub type PrivateDivIfQuot<N, D, Q, R, I, RcmpD> =
        <() as PrivateDivIf<N, D, Q, R, I, RcmpD>>::Quotient;
    pub type PrivateDivIfRem<N, D, Q, R, I, RcmpD> =
        <() as PrivateDivIf<N, D, Q, R, I, RcmpD>>::Remainder;

    // Div for signed ints
    pub trait PrivateDivInt<C, Divisor> {
        type Output;
    }
    pub type PrivateDivIntOut<A, C, Divisor> = <A as PrivateDivInt<C, Divisor>>::Output;

    pub trait PrivateRem<URem, Divisor> {
        type Output;
    }
    pub type PrivateRemOut<A, URem, Divisor> = <A as PrivateRem<URem, Divisor>>::Output;

    // min max
    pub trait PrivateMin<Rhs, CmpResult> {
        type Output;
        fn private_min(self, rhs: Rhs) -> Self::Output;
    }
    pub type PrivateMinOut<A, B, CmpResult> = <A as PrivateMin<B, CmpResult>>::Output;

    pub trait PrivateMax<Rhs, CmpResult> {
        type Output;
        fn private_max(self, rhs: Rhs) -> Self::Output;
    }
    pub type PrivateMaxOut<A, B, CmpResult> = <A as PrivateMax<B, CmpResult>>::Output;

    // Comparisons

    use {Equal, False, Greater, Less, True};

    pub trait IsLessPrivate<Rhs, Cmp> {
        type Output: Bit;
    }

    impl<A, B> IsLessPrivate<B, Less> for A {
        type Output = True;
    }
    impl<A, B> IsLessPrivate<B, Equal> for A {
        type Output = False;
    }
    impl<A, B> IsLessPrivate<B, Greater> for A {
        type Output = False;
    }

    pub trait IsEqualPrivate<Rhs, Cmp> {
        type Output: Bit;
    }

    impl<A, B> IsEqualPrivate<B, Less> for A {
        type Output = False;
    }
    impl<A, B> IsEqualPrivate<B, Equal> for A {
        type Output = True;
    }
    impl<A, B> IsEqualPrivate<B, Greater> for A {
        type Output = False;
    }

    pub trait IsGreaterPrivate<Rhs, Cmp> {
        type Output: Bit;
    }

    impl<A, B> IsGreaterPrivate<B, Less> for A {
        type Output = False;
    }
    impl<A, B> IsGreaterPrivate<B, Equal> for A {
        type Output = False;
    }
    impl<A, B> IsGreaterPrivate<B, Greater> for A {
        type Output = True;
    }

    pub trait IsLessOrEqualPrivate<Rhs, Cmp> {
        type Output: Bit;
    }

    impl<A, B> IsLessOrEqualPrivate<B, Less> for A {
        type Output = True;
    }
    impl<A, B> IsLessOrEqualPrivate<B, Equal> for A {
        type Output = True;
    }
    impl<A, B> IsLessOrEqualPrivate<B, Greater> for A {
        type Output = False;
    }

    pub trait IsNotEqualPrivate<Rhs, Cmp> {
        type Output: Bit;
    }

    impl<A, B> IsNotEqualPrivate<B, Less> for A {
        type Output = True;
    }
    impl<A, B> IsNotEqualPrivate<B, Equal> for A {
        type Output = False;
    }
    impl<A, B> IsNotEqualPrivate<B, Greater> for A {
        type Output = True;
    }

    pub trait IsGreaterOrEqualPrivate<Rhs, Cmp> {
        type Output: Bit;
    }

    impl<A, B> IsGreaterOrEqualPrivate<B, Less> for A {
        type Output = False;
    }
    impl<A, B> IsGreaterOrEqualPrivate<B, Equal> for A {
        type Output = True;
    }
    impl<A, B> IsGreaterOrEqualPrivate<B, Greater> for A {
        type Output = True;
    }

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